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What is the area of triangle ABC above, with side lengths x,y, and z?
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Updated on: 02 Jul 2019, 07:53

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Question: (1/2) xy=?Here, (1/2) is fixed numerical term.So, if we find the value of xy, we can can easily find the value of (1/2) xy i.e. AREA of the triangle.SO, WE SIMPLY NEED the value of xy. Thus, question becomes xy=?

Re: What is the area of triangle ABC above, with side lengths x,y, and z?
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02 Jul 2019, 08:31

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Solution:

Question Stem analysis:

Triangle ABC is a right angled triangle making AB represented as x as it's height, and BC represented by y as it's base. Area of the triangle is 1/ X Base X Height Therefore we need the values of x & y to identify he area.

Statement one alone:

(x + y)^2 - (x - y)^2 = 80, when we solve this, we get 4xy = 80 & xy=20 Hence we can find out the area of the triangle which comes to 10We can safely eliminate choices B,C & E.

Statement 2 alone:

(x - y)= 1Clearly, this statement is not sufficient to find out the values of x & y, Thus statement two alone is not sufficient.Hence the answer is A
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Re: What is the area of triangle ABC above, with side lengths x,y, and z?
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02 Jul 2019, 08:33

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Question: What is the area of triangle?

Observations:The given image is a right angled triangle with the sides x,y,z. Consider, base = y, and height = xArea of Triangle = (1/2)*base*height = (x*y)/2

Statement 1: (x+y)\(^2\)−(x−y)\(^2\)=80. Simplifying this,x\(^2\)+y\(^2\)+2xy-x\(^2\)-y\(^2\)+2xy = 804xy = 80. From this we can easily find (x*y)/2 which is the area of the triangle. Remember we don't need to find the exact value in DS problems, we just need to have one true answer and we have it.Therefore Statement 1 is sufficient. ---> AD/BCE

Statement 2: (x−y)=1In this case, x and y can take more than one single value and still make the statement true. In this case, we don't need to find the value of z even though it is easy because we don't need it.

For example, when x=4, y=3 -> Area of triangle = 6when x=5, y=4 -> Area of triangle = 10.